Yes, she shows her face a lot actually. She just has a fear of showing it in videos and the like because she's not too confident in how she is perceived by others. This is mainly because she is shy and because she dislikes the idea of being famous for looks and not her art.
When people get famous, they tend to get associated with their faces and what they do in their personal life instead of their art. This is especially true in this kind of music. That's why it's kind of easy to understand why she wants to be known for her art, and not the way she looks. Not to mention when you're a famous face, people are going to not let you live your day to day life and will always be bothering your for autographs and the like.
I will include a video with her making all kinds of silly faces with her real face, and also here's a picture of her at an event:
1 - http://hollywoodlife.com/2015/02/10/sia-face-why-she-doesnt-show-hates-fame/